The value of the probability P(E and F) is 0.2802
Independent probabilityEvents are known to be independent if the occurrence of one does not affect the other.
Given the following parameters
P (E) =0.471
P(F) = 0.595
If E and F are independent, then;
P(E and F) = P(E)P(F)
P(E and F) = 0.471 * 0.595
P(E and F) = 0.2802
Hence the value of the probability P(E and F) is 0.2802
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Angles X, Y, and Z are supplementary. The sum of the measure of Angles X and Y is 3 more than double the measure of Angle Z. What is the measure of Angle Z
Answer:
59 degrees
Step-by-step explanation:
Supplemental means that the angles add to 180.
x + y + z = 180
x + y = 2z + 3
Replace x + y in the top equation with 2z + 3
2z + 3 = z = 180
3x + 3 = 180 Combine the z's.
3x = 177 subtract 3 from both sides
x = 59
An insurance policy sells for $600. Based on past data, an average of 1 in 50 policy holders
will file a $5,000 claim, an average of 1 in 100 policyholders will file a $10,000 claim, and an average
of 1 in 200 policyholders will file a $30,000 claim.
(a) Find the expected value (to the company) per policy sold.
(b) If the company sells 10,000 policies, what is the expected profit or loss?
Using the expected value of a discrete distribution, the values are given as follows:
a) $250.
b) $2,500,000.
What is the mean of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
The distribution of the company's earnings is given as follows:
P(X = -4400) = 0.02.P(X = -9400) = 0.01.P(X = -29400) = 0.005.P(X = 600) = 0.965.Considering that the policy sells for $600, for example, a $5000 claim is a loss of $5000 - $600 = $4,400 for the company, which explains the above distribution.
Item a:
The expected value for a policy sold is given by:
E(X) = 600(0.965) - 4400(0.02) -9400(0.01) - 29400(0.005) = 250.
Item b:
Considering the value found in item a for a single policy, for 10,000 policies, the expected profit is given by:
E = 10000 x 250 = 2,500,000.
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( will give brainliest)
How many 4-letter words with at least one vowel can be constructed from the letters A, B, C, D, and E? (Note that A and E are vowels, any word is valid, not just English language words, and letters may be used more than once.)
Answer:
544 words
Step-by-step explanation:
The number of 4 letter words can be constructed from ABCDE would be 5^4 = 625
The number of 4 letter words can be constructed using BCD would be 3^4 = 81
So the number of words that use at least one vowel would be 5^4 - 3^4 = 625-81 = 544
Recently, a certain bank offered a 10 year CD that earns 2.97% compounded continuously.
Use the given information to answer the questions:
Using continuous compounding, it is found that:
a) The account will be worth $26,916.31 in 10 years.
b) It will take 42.18 years for the account to be worth $70,000.
What is compound interest?The amount of money earned, in continuous compounding, after t years, is given by:
[tex]A(t) = Pe^{rt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value).The parameters are given as follows:
A(0) = 20000, r = 0.0297, t = 10.
Hence the worth in 10 years will be given by:
[tex]A(t) = Pe^{rt}[/tex]
[tex]A(10) = 20000e^{0.0297 \times 10}[/tex]
A(10) = $26,916.31.
Now, we find in how many years it will be worth $70,000, as follows:
[tex]A(t) = Pe^{rt}[/tex]
[tex]70000 = 20000e^{0.0297t}[/tex]
[tex]e^{0.0297t} = 3.5[/tex]
[tex]\ln{e^{0.0297t}} = \ln{3.5}[/tex]
[tex]0.0297t = \ln{3.5}[/tex]
[tex]t = \frac{\ln{3.5}}{0.0297}[/tex]
t = 42.18 years.
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What’s LCM of 4 and 18
Answer:
2²X3³=36
Step-by-step explanation:
hope this helps you (✿❛◡❛)
Lydia has half of her investments in stock paying an 11% dividend and the other half in a stock paying 14% interest. If her total annual interest is $440, how much does she have invested?
Answer
Based on the calculations, the amount of money she invested is equal to $3,520.
How to determine the amount invested?First of all, we would assign variables to the amount of money that he invested at different interest rates as follows:
Let x be the amount of money she invested at 11%.Let y be the amount of money she invested at 14%.Since Lydia invested the same amount of money in both stocks, we have:
x = y ....equation 1.
At the two interest rates, the total amount Lydia gets is given by:
0.11x + 0.14y = 440 ....equation 2.
Solving the equations simultaneously, we have:
0.11y + 0.14y = 440
0.25y = 440
y = 440/0.25
y = $1,760.
Thus, the total investment is given by:
Total investment = 1760 + 1760
Total investment = $3,520.
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i need help plsssss asap
Answer:
D) (0,9.5) and (10,1.5)
Step-by-step explanation:
a line of best fit is a line that is drawn through the data points on the scatter plot. Option D is the only answer that draws a linear line through the data points.
Option A makes a short line above the points. if the line is not through the points, it doesn't work
Option B is drawing a positive line (as in it's increasing) and therefore cannot work
Option C draws a line below the points and does not represent the line of best fit for this scatter plot
Find n in this equation: 308P(n,2)=P(16,4)
Answer:
24
Step-by-step explanation:
7x4
The Mega Millions lottery is available in multiple states including New Jersey. A Mega Millions ticket consists of 5 different numbers from 1 to 70, followed by the "Mega Ball" number which is a number 1 to 25. To win the jackpot the player must match all 6 numbers (the 5 chosen from 1 to 70, and the Mega Ball number). The order of the numbers does not matter. If you were to purchase a single ticket, what is the probability that you'll win the jackpot?
A. 1/302575350
B. 1/42017500000
C. 1/36309042000
D. 1/12103014
Using the combinations formula, the probability that you'll win the jackpot is given by:
A. 1/302575350.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
5 numbers are selected from a set of 70, along with one number from a set of 25, hence the number of combinations is given by:
[tex]C_{70,5}C_{25,1} = \frac{70!}{5!65!} \times \frac{25!}{1!24!} = 302575350[/tex]
Only one combination is correct, hence the probability of winning is given by:
A. 1/302575350.
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Which diagram shows the medians of a triangle?
triangle 1
triangle 3
O A. triangle 1
OB. triangle 2
OC. triangle 3
OD. triangle 4
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triangle 2
triangle 4
medians of a triangle is triangle 4
1. La Sra. Hamilton quiere comprar pizarras y marcadores para su salón de
clases. Los tableros (b) cuestan $0.75 cada uno y los marcadores (m) cuestan
$0.50 cada uno. Escribe una expresión que muestre la cantidad total que
gastará en pizarras y marcadores.
Usando un sistema de ecuaciones, se encuentra que la expresión que muestra la cantidad total que gastará en pizarras y marcadores es:
G = 0.75b + 0.5m.
¿Qué es un sistema de ecuaciones?
Un sistema de ecuaciones es cuando dos o más variables están relacionadas y las ecuaciones se construyen para encontrar los valores de cada variable.
En este problema, las variables son:
Variable b: Cantidad de tableros.Variable m: Cantidad de marcadores.Considerando el precio de cada producto(cada tablero = $0.75, cada marcador = $0.5), la expresión que muestra la cantidad total que gastará en pizarras y marcadores es:
G = 0.75b + 0.5m.
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You know the area (A = 300 ft^2) and the width (w = 4 ft), but not the length. Rewrite the formula by dividing both sides by the width.
length = Answer
Answer:
Length equals to 75 ft
Step-by-step explanation:
A=l x w Area of a rectangle formula.
A/w=l Solve for length
300=l x 4
300=l x 4
4 4
300/4=l
75=l
7+5y=-13 solve for y
[tex]\large\displaystyle\text{$\begin{gathered}\sf 7+5y=-13 \end{gathered}$}[/tex]
Subtract 7 from both sides.
[tex]\large\displaystyle\text{$\begin{gathered}\sf 5y=-13-7 \end{gathered}$}[/tex]
Subtract 7 from −13 to get −20.
[tex]\large\displaystyle\text{$\begin{gathered}\sf 5y=-20 \end{gathered}$}[/tex]
Divide both sides by 5.
[tex]\large\displaystyle\text{$\begin{gathered}\sf y=\frac{-20}{5} \end{gathered}$}[/tex]
Divide −20 by 5 to get −4.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf y=-4 \end{gathered}$} }\large\displaystyle\text{$\begin{gathered}\sf \ \ \to \ \ \ Answer \end{gathered}$}[/tex]
VerificationWe let y = -4.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{7+5\times-4=-13 \ \ \to \ \ [ Multiply] } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{7-20 \ \ \to \ \ [Subtract] } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-13=-13 \ \ \to \ \ [ Equality \ holds ]} \end{gathered}$}[/tex]
{ Pisces04 }Answer:
5y= -13-7
5y=-20
5y = -20
5 = 5
y = -4
the range of the function?
1 2
2 4
3 9
4 16
Answer:
2,4,9,16
Step-by-step explanation:
2
4
9
16
are range because they are exactly opposite of domain
una familia compuesta por 4 personas van a celebrar el cumpleaños de su hijo para lo cual compran una torta y realizan el siguiente reparto: una familia compuesta por 4 personas van a celebrar el cumpleaños de su hijo para lo cual compran una torta y realizan el siguiente reparto: la mamá recibe 1/7 de pastel; el papá recibe 3/14 de pastel; el hijo mayor recibe 2/7de pastel; ¿qué cantidad recibió el cumpleañero?
Durante la celebración familiar del cumpleaños y aplicando las propiedades de los números fraccionarios, el hijo menor recibió 5/14 de la torta.
¿Cuánta proporción del pastel recibió el cumplimentado?
En esta pregunta tenemos una torta de cumpleaños, que asumimos de forma circular. Si leemos con cuidado el enunciado, encontramos que la proporción del pastel correspondiente al cumplimentado mediante la siguiente sustracción de fracciones:
x = 1 - 1/7 - 3/14 - 2/7
x = 6/7 - 3/14 - 2/7
x = 4/7 - 3/14
x = 8/14 - 3/14
x = 5/14
Durante la celebración familiar del cumpleaños y aplicando las propiedades de los números fraccionarios, el hijo menor recibió 5/14 de la torta.
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Lucas spends $83.42 in additional interest and charges on monthly payments as the result of a prior bankruptcy. if lucas been able to save this money for the year and then put it into a savings account earning 1.8% simple interest, how much money could he have in savings after 3 more years? a. $1,649.72 b. $1,055.10 c. $1,019.06 d. $1,001.04 please select the best answer from the choices provided a b c d
Hence, the correct answer is (c)$1,055.10
What is simple interest?Simple interest is interest calculated on the principal portion of a loan or the original contribution to a savings account. Simple interest does not compound, meaning that an account holder will only gain interest on the principal, and a borrower will never have to pay interest on interest already accrued.
How to solve?We have,
Amount spent each month = $83.42
Interest rate, r = 1.8% = 0.018
Time, n = 3 years
Now,
The total amount collected at the end of the year = $83.42 × 12 = $1001.04
The value of the amount deposited in the bank after 3 years will be
Future value = Present value × ( 1 + r )ⁿ
on substituting the respective values,
we have
Future value = $1001.04 × ( 1 + 0.018 )³
or
Future value = $1,056.07
Hence,
The money he could have at the end of 3 more years will be $1,055.17
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please help me with this!!!!!!!!!!
Answer: 5 rides (for a cost of $35)
Step-by-step explanation:
The solution to your problem is the point of intersection. This is where the lines intersect, or cross over, each other. We can extend the lines to find the answer. See attached.
They intersect at point (5, 35) which represents 5 rides and 35 dollars.
A group of people were asked if they had run a red light in the last year. 198 responded "yes", and 394 responded "no".
Find the probability that if a person is chosen at random, they have run a red light in the last year.
Give your answer as a fraction or decimal accurate to at least 3 decimal places
Choose the system of inequalities that best matches the graph below.
The system of equations represented by the graph is the one in option b.
Which is the graphed system of equations?We can see that the graph is:
A solid line with a positive slope, such that the region above the line is shaded.
This is represented by:
y ≥ line.
And we can see a horizontal line at y = 4, the line is dashed and the region below the line is shaded, then we have:
y < 4
Then the system is of the form:
y ≥ line.
y < 4
The only option that has that form is option B, so that is the correct one.
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Write an equation of a circle with the given center and radius
Center(-7,-6) Radius = 2
The equation of the circle is (x + 7)² + (y + 6)² = 4 if the center and radius are (-7,-6) and 2 respectively.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have center of the circle(h, k) = (-7, -6)
The radius of the circle r = 2
The standard form of a circle:
(x - h)² + (y - k)² = r²
(x - (-7))² + (y - (-6))² = 2²
(x + 7)² + (y + 6)² = 4
Thus, the equation of the circle is (x + 7)² + (y + 6)² = 4 if the center and radius are (-7,-6) and 2 respectively.
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Please can u help me?
Answer:
6/2^2=36/4
so it will be 36/4+14/1
taking LCM As 4 it will come out
36+56/4 =92/4=23
Step-by-step explanation:
hope this helps ʕ´•ᴥ•`ʔ
Answer:
23
Step-by-step explanation:
(6/2) ^2 +7*2
We need to solve this using the order of operations
First, solve the item in parentheses
6/2 =3
(3) ^2 +7*2
Then calculate the exponential term
3^2 = 9
9 + 7*2
Then multiply
7*2 = 14
9+14
Finally add
23
Given the function f(x) = −3x2 + 4x + 6, find f(2) and f(3). Choose the statement that is true concerning these two values.
The value of f(2) is the same as the value of f(3).
The value of f(2) cannot be compared to the value of f(3).
The value of f(2) is smaller than the value of f(3).
The value of f(2) is larger than the value of f(3).
PLEASE Help NOW
The true statement is the value of f(2) is larger than the value of f(3).
How to evaluate the function?The function is given as:
f(x) = −3x^2 + 4x + 6
Calculate f(2) and f(3), as follows:
f(2) = −3(2)^2 + 4(2) + 6 = 2
f(3) = −3(3)^2 + 4(3) + 6 = -9
By comparison;
f(2) is greater than f(3) because 2 > 9
Hence, the true statement is the value of f(2) is larger than the value of f(3).
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Estimate the average rate of change from x=3 to x=7 .
[tex]f(3) = 1 \: \: \: \: \: \: \: \: f(7) = 3[/tex]
[tex] \frac{f(7) - f(3)}{7 - 3} = \frac{3 - 1}{4} = \frac{2}{4} = 0.5[/tex]
If f(x) = x^3 and g(x) = -2x^3, how has f(x) been transformed to get g(x)?
a.The graph of f(x) has been reflected across the x-axis and shifted up 2 places
b.The graph of f(x) has been reflected across the y-axis and shifted down 2 places
c.The graph of f(x) has been reflected across the x-axis and shifted left 2 places
d.The graph of f(x) has been reflected across the y-axis and shifted right 2 places
e.The graph of f(x) has been reflected across the y-axis and stretched by a factor of 2
The graph of f(x) has been reflected across the y-axis and stretched by a factor of 2 , Option E is the correct answer.
What is a Function ?A function is a law that relates a dependent and an independent variable.
It is given that f(x) = x³
g(x) = -2x³
When a function is reflected along an axis , the coordinate of that axis remains the same but the coordinate of the other axis becomes negative
So, if x coordinate is transformed to -ve of the parent function , The function is reflected along y axis.
As there is 2 in front of the parent function ,
f'(x) = a f(x) , represents vertical stretch when a >1
Therefore The graph of f(x) has been reflected across the y-axis and stretched by a factor of 2 , Option E is the correct answer.
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list the angles of ABC in order from smallest to largest
The size of a triangle side is proportional to its opposite angle. The largest side is opposite to the largest angle while the smallest side is opposite to the smallest angle.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The size of a triangle side is proportional to its opposite angle. The largest side is opposite to the largest angle while the smallest side is opposite to the smallest angle.
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PLEASE HELP EMERGENCY
Estimate the length of wire to the nearest inch. Suppose that it is coiled 11 times. Which numbers did you use to estimate the length of wire in the question above? Explain your process of estimation.
242 inches
Step-by-step explanation:
with an 11 inch diameter, a single spiral of the wires circumference is about 22 inches. with this we can multiply 22 by 11 and assume its 242 inches long
in your own words , what is drecrete math
Answer:
Discrete mathematics is the study of mathematical structures that can be considered "discrete" rather than "continuous". Objects studied in discrete mathematics include integers, graphs, and statements in logic.
A cook needs 7 cups of vegetable stock for a soup recipe. How much is this in pints? Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer. Ú 08 Explanation Check fl oz qt X values: One... gal pt S .? © 2022 McGraw HilllLS ALL
Answer:
3 1/2 pints
Step-by-step explanation:
A pint is two cups
7 cups / 2cups/pint = 7/2 pint = 3 1/2 pints
mrs sen has a swuare piece of cloth of side 100 cm.how many square pieces of cloths of sude 25 cm can be cut from the cloth
Answer:
16 pieces
Step-by-step explanation:
(100*100)-(25*25)=16
Solve for x. Round to the nearest hundredth if necessary.
Answer:
Step-by-step explanation:
[tex]\frac{19}{x}[/tex] = tan 29°
x = [tex]\frac{19}{tan29^o}[/tex] ≈ 34.28